Improve mouse movement performance

[enaboapps]

Summary

• optimize the continuous mouse movement path with relative SendInput movement and damping
• cache display and cursor overlay settings during high-frequency input
• throttle LastSeenAt persistence and move Bluetooth command handling off the WPF dispatcher

Fixes #381.

Validation

• dotnet restore src/SwitchifyPc.sln
• dotnet build src/SwitchifyPc.sln -c Release --no-restore
• dotnet test src/SwitchifyPc.sln -c Release --no-build
• manual dev build launch and Android movement feel check